Rectangle RSTU is shown below. The rectangle was dilated by a scale factor of 1/3. After the dilation, what is the perimeter of R'S'T'U'?

Question

The coordinates of RSTU are

R ----> (-5,4)

S ----> (4,4)

T ----> (4,-2)

U ----> (-5,-2)

Answer 1

A dialtion by a scale factor of 1/3 means we multiply the coordinates of each vertex by 1/3.

R ---> (-5/3,4/3)

S ---> (4/3,4/3)

T ---> (4/3,-2/3)

U ---> (-5/3,-2/3)

If we look at the vertical line between R and U or S and T, we see the distance is 4/3 - (-2/3) = 6/3 = 2

The horizontal line between R and S or T and U has a distance of 4/3 - (-5/3) = 9/3 = 3

2(2 + 3) = 2(5) = 10

Answer 2

Step 1. Figure out the length of the sides of the original figure RSTU. RS and TU are each 9 units long and RU and ST are both 6 units long. That means the perimeter is 30 (9 + 9 + 6 + 6 = 30)

Step 2: multiply the perimeter by the scale factor. 30 x 1/3 = 10 so the perimeter of the dilated rectangle is 10